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Students compose the image functions they’ve learned, applying their knowledge of coordinates to position differently-shaped and transformed images to create flags of varying complexity.

Lesson Goals

Students will be able to:

  • Put one image on top of another, using the put-image function.

  • Decompose complex images into parts.

  • Combine and manipulate images to create more complex images.

Student-facing Goals

  • I can put one image on top of another.

  • I can make complex images like flags.

Materials

Supplemental Resources

Preparation

  • Make sure all materials have been gathered.

  • Decide how students will be grouped in pairs.

  • For some students, the use of graph paper for this activity will make a big difference!

Key Points For The Facilitator

  • The put-image function treats the second image as the first quadrant of a cartesian plane. Having students sketch their flag on a sheet of graph paper drives this point home, and makes the programming easier.

  • This is an excellent opportunity to introduce students to indenting code. The difference between poorly-indented flag code and well-indented flag code is extremely noticable.

Language Table

Types

Functions

Values

Number

+, -, *, /, expt, sqr, sqrt

4, -1.2, 2/3, pi

String

string-length, string-repeat, string-contains?

"hello", "91"

Boolean

<, <>, <=, >=, string<?, string>?, string=?, string<>?, string>=?

true, false

Image

star, triangle, circle, square, rectangle, rhombus, ellipse, regular-polygon, radial-star, text, overlay, above, beside, rotate, scale, flip-horizontal, flip-vertical

🔵🔺🔶

Glossary
contract

a statement of the name, domain, and range of a function

🔗Putting Images Together 25 minutes

Overview

Students learn about the put-image function.

Launch

As you’ve already seen, overlay sticks two images together, so that the center of the first image is placed exactly on top of the center of the second image. But what if we want to put the dot somewhere besides the center?

The put-image function works like overlay, but instead of placing the centers of each image on top of one another, it translates the center of the top image by some distance in the x- and y-direction.

Think of the background image as a sheet of graph paper with the origin (0,0) in the bottom left corner.

The numbers in put-image specify a point on that graph paper, with the center of the top image being placed there.

  • Distribute Estimating Coordinates (Page 37) or project the flag images from the peardeck.

  • The code beneath each image is missing the x and y coordinates to place the dot.

  • Estimate the x- and y-coordinate of the dot’s location for each image and complete the code!

Investigate

Have students open the Flags Starter File , and click Run.

There are some special lines in this file called comments. The programmer who wrote this code included a series of messages - called comments - that will never be read by the computer.

Professional programmers use comments all the time.

Professional programmers work with teams who need to be able to follow each other’s thinking in order to collaborate efficiently. Comments are a way for programmers to leave notes for one another, and even for a single programmer to keep track of their thinking when they come back to their code another day.

  • Each language has its own symbol for commenting. In WeScheme, we use the semi colon (;) to tell the computer to ignore what we’re typing. What color does the code turn when it has a semicolon in front of it? Purple!

  • Type japan-flag into the Interactions Area. What do you get back?

  • Type japan into the Interactions Area and compare the image to japan-flag.

  • japan is composed using dot and background. Type each of those variables into the Interactions Area. What do you get back?

  • Take a look at the japan code and fix it so that it matches the japan-flag image.

  • What is the Contract for put-image? (Write it in your Contracts page!)

Have students open the Flags of Netherlands, Ireland, Mauritius Starter File , and click Run.

  • Look at the code for the flag of the Netherlands.

  • How big is the flag?

  • What was the programmer thinking when she coded the height of the red stripe as (/ 200 3)?

  • The center of the blue stripe is placed at (150, (/ 200 6)).

  • How did the programmer know to use 150 as the x-coordinate?

  • What was the programmer thinking when she coded the y-coordinate as (/ 200 6)?

  • Explain the thinking behind coding the redstripe’s y-coordinate as (* 5 (/ 200 6)).

Once you’ve discussed the code for the flag of the Netherlands with your class, have them keep working with this starter file to write code for the flags of Ireland and Mauritius. Some students will make it through the challenges. Some students may only complete one flag. All of them will be synthesizing how to apply put-image and locate images on the coordinate grid.

Synthesize

Could we completely replace overlay with put-image? Why or why not?

Going Deeper

If you have time, we have lots of additional starter files to push student thinking linked in the additional exercises at the end of this lesson and now would be the time to dive into them!

🔗Making Flags 25 minutes

Overview

Students focus on decomposing complex images into simple ones, and using put-image to combine them.

Launch

Let’s dig into the process for how the flags we’ve seen so far were made:

1) Decompose the Image

We observe that the Japanese flag is made up of two simpler images: a black, outline rectangle and a red dot.

2) Define those parts

We define dot and background. Once we’ve defined those images, we test them out in the Interactions Area to make sure they look right!

3) Find the Coordinates

For each image, calculate what the x- and y-coordinates of the center should be. TIP: this is a lot easier if you have a sheet of graph paper handy!

4) Build the Image & Check that it Matches the Target Image

We stack the parts on top of the bottom image using the coordinates we found. TIP: don’t cram all the code into one line! If you break it up into new lines (for example, hitting "Return" before the x-coordinate and after the y-coordinate), you’ll notice that the code forms a "staircase" pattern. Be sure to compare the image you get with the target image!

If you have time, these matching activities will support student thinking.

Investigate

Paper Flag Models to Code In this next exercise, students will be decomposing the image of a flag. For a more tactile experience, you could have students construct images of the flags they choose using construction paper. This should happen between the step where they describe the shapes needed to compose the flags image and write the code to build the image. The act of physically building the flag from layers of paper makes the layering of the coded images visible and helps students to remember that white space is not just "blank".

  • Turn to Decomposing Flags (Page 38), and choose ONE flag to focus on. On the blank lines below, describe the parts that make up that flag.

  • Once you’re done, return to the Flags Starter File and define those parts.

  • Then, compose those parts using put-image, and make your flag!

Around the World in your Classroom The opportunity to focus on a flag of their choosing is a big motivator for students. Coding flags also presents a rare opportunity for students to share a piece of their identity in math class. If you have more time to devote, we highly encourage you to give students the opportunity to create the image of a flag they connect with in some way. Students might choose the flags of countries related to their heritage, a place they’ve visited, a country they’re interested in, or a group they identify with or support. Encourage students to choose an appropriately challenging flag. The teacher may introduce parameters if necessary, such as “Flags need at least 5 different shapes”. This is intended to be a summative project, so encourage students to demonstrate what they’ve learned. Once students have coded their flags, host a tour of the flags of the world in your classroom!

Be mindful of the fact that not every student will know their family’s geographical history, and that immigration can be a sensitive topic for some students. For this reason, it is important that students have the option to choose a flag based on interest instead of just family history.

Be prepared that students might choose flags representing groups other than countries. Indigenous students might choose a flag that represents their indigenous nation or the American Indian Movement. Students might also choose to focus on the pride flag (representing solidarity amongst members of the LGBTQ community) or an ethnic flag (representing solidarity amongst members of different ethnic groups, such as the Hispanic flag). There are also some flags that represent political or activist groups. It is important for the teacher to be open to different beliefs and ideologies, but it is also up to the teacher’s discretion as to whether or not a flag is appropriate for use in this project. Flags associated with hate groups, or any institution that denies the dignity of other students, are not appropriate.

Flags of the World and Flag Wizard may be useful to students looking for ideas. Flags are listed with their width:length ratios in the opposite order of how we define the sides of a flag in code. e.g. 2:3 could be scaled up to a 300 x 200 flag or 8:11 could be scaled up to 330 by 240.

Ratio and Proportion

Have students define the WIDTH and HEIGHT of their flags as values, and then replace the numbers in each flag with expressions relative to width and height. For example, if the dot in the Japanese flag is at (150, 100), those numbers would be replaced with (/ WIDTH 2) and (/ HEIGHT 2).

Synthesize

Which flags were the easiest to make? The hardest?

Why is it useful to define each part of the flag first, before stitching the images together?

🔗Additional Exercises

These materials were developed partly through support of the National Science Foundation, (awards 1042210, 1535276, 1648684, and 1738598). CCbadge Bootstrap:Algebra by the Bootstrap Community is licensed under a Creative Commons 4.0 Unported License. This license does not grant permission to run training or professional development. Offering training or professional development with materials substantially derived from Bootstrap must be approved in writing by a Bootstrap Director. Permissions beyond the scope of this license, such as to run training, may be available by contacting contact@BootstrapWorld.org.